Question

If PR = 4 and RS = 5, what if PQ?

Answer 1

The measure of the tangent line PQ to the circle is 6 units.

To solve for the length of PQ, we use the secant-tangent power theorem:

( tangent segment )² = External part of the secant segment × Secant segment.

Given that:

Tangent segment = PQ = ?

The external part of the secant segment = PR = 4

Secant segment = PR + RS = 4 + 5 = 9

Plug these values into the above formula and solve for the tangent line PQ:

( PQ )² = PR × ( PR + RS )

( PQ )² = 4 × ( 9 )

( PQ )² = 36

PQ = √36

PQ = 6 units

Therefore, segment PQ measures 6 units.

Answer 2

Given,

The measure of line segment PR is 4.

The measure of line segment RS is 5.

We know that,

By the relaation of tangent ans secant

`PQ^2=PR*(PR+RS)`

Subsituting the values then,

`\begin{gathered} PQ^2=4*(4+5) \\ PQ^2=4*9 \\ PQ^2=36 \\ PQ=6 \end{gathered}`

Hence, the measure of tangent PQ is 6